Computer-implemented method for determining behaviour and load parameters of soft tissue from a plurality of images acquired in different vertical orientations

Abstract

The invention relates to a computer-implemented method for determining parameters comprising a stiffness field of soft tissue ( α ) and a load parameter ( p ) applied to the soft tissue, in particular a pressure field, which comprises determining, from at least two images of this soft tissue oriented in at least two different respective positions with respect to the vertical direction, the values ( α1, p1) of these parameters that make it possible to minimise a deviation between the deformations of at least one portion of the soft tissue observed from the images and the corresponding deformations determined by a model ( U ( α , p )) of the soft tissue which depends on these parameters.

Description

[0001] Description

[0002] Title: Computer-implemented method for determining behavioral and loading parameters of soft tissue from a plurality of images acquired in different vertical orientations

[0003] Technical field

[0004] The present invention relates to the field of estimation of behavioral and loading parameters of soft tissue models from images.

[0005] The invention relates more specifically to a computer-implemented method for determining a stiffness field of a soft structure and a loading parameter such as a force or pressure field applied to this structure, combining several images acquired in different orientations.

[0006] The main area of ​​application envisaged is biomedical engineering, more specifically personalized numerical modeling applied to the diagnosis, classification, prognosis and treatment of patients. The invention is particularly suitable for the in vivo and non-invasive estimation of stiffness and pressure applied to soft living tissues.

[0007] More generally, the invention can be applied to all objects or soft tissues, whether human, animal or plant, to non-invasively estimate internal rigidities and pressures, as well as other parameters inherent to a model, from volume images, without requiring force measurement.

[0008] Prior art

[0009] The construction of digital models of biological tissues is an active field of biomechanics. Such models can provide medical professionals with reliable tools to aid in the prognosis or diagnosis of pathologies as well as in monitoring the progress of medical treatments. Personalized digital models, also called "digital twins," are particularly advantageous. They involve coupling the physical modeling of a tissue with specific data obtained on a patient to obtain a precise, objective, and quantitative view of the patient's condition.

[0010] The creation of a digital model of a tissue is based on the definition of a constitutive law, which describes the behavior of the modeled tissues and involves so-called constitutive material parameters such as the stiffness of the tissue, in combination with a loading, i.e. the stresses to which the tissue is subjected. The loading involves parameters such as the force or pressure field imposed on the tissue which are typically either fixed to standard physiological values ​​empirically, or estimated from information extracted from data collected on the tissue.

[0011] When building digital twins, it is usually not possible to identify all parameters of a complex tissue or organ model from clinical images. Therefore, it is often necessary to fix parameters to physiological values.

[0012] This solution is, however, unsatisfactory. Indeed, the material parameters as well as the loading parameters, in particular the internal pressure field when present, vary very strongly from one individual to another. In addition, the physiological data generally come from ex vivo experiments, possibly conducted on animals, which introduces a significant bias into the experimental parameter values ​​obtained.

[0013] The use of acquired data is therefore important for the production of personalized numerical models, in particular to take into account the great variability of parameters between individuals. Estimating parameters from measurements, when possible, remains the most reliable solution for the construction of data-based models.

[0014] However, it is generally not possible to identify constitutive parameters or loading parameters solely from images, since a force measurement is required to complement the kinematic data present in the images. In particular, the absence of internal tissue force measurements prevents the correct identification of constitutive parameters.

[0015] In particular, it is generally difficult to measure the value of the internal pressure applied to certain tissues, even though this pressure can constitute an important biomarker for the diagnosis and prognosis of pathologies. This is the case, for example, of the lung, subjected to pleural pressure, i.e., a negative pressure keeping the lungs inflated, for which in vivo measurement is very difficult. The classic method for measuring this pressure consists of the use of esophageal balloons. This method is, however, both too imprecise and too invasive to be carried out in routine surgery.

[0016] The article Visentin, F., Groenhuis, V., Maris, B., Dall'Alba, D., Siepel, F., Stramigioli, S. & Fiorini, P. (2019). Iterative simulations to estimate the elastic properties from a series of MRI images followed by MRI-US validation. Medical & Biological Engineering & Computing describes the use of MRI images in the context of breast deformation modeling to estimate the stiffness of a physical reproduction of a breast. The images are obtained by placing the breast model in two different positions. The deformation of the model is due solely to gravity. The comparison between the obtained images allows the estimation of the model's stiffness.

[0017] At equilibrium, the remote forces, in this case gravity, balance with the contact forces, also called reaction forces, exerted by the surrounding systems. Reaction forces are not considered in this article. Furthermore, the boundary conditions at the base of the breast are not representative of real physiological conditions because the displacements are completely blocked. Therefore, it is not possible to correctly estimate the reaction forces. Furthermore, the described method is not applicable to the case of strongly moving tissues. The edges of a lung, for example, move strongly between the end-expiratory configuration and the end-inspiratory configuration.

[0018] Thus, the solution described is not intended to estimate the loading to which the organ studied is subjected.

[0019] There is therefore a need to propose methods for estimating behavioral parameters but also loading parameters, allowing the construction of more reliable digital twins.

[0020] The aim of the invention is to meet this need.

[0021] Statement of the invention

[0022] To this end, the invention relates to a computer-implemented method for determining parameters comprising a stiffness field of a soft tissue (a) and a loading parameter (p) applied to the soft tissue, in particular a pressure field, in which the values ​​are determined from at least two images of this soft tissue oriented in at least two different respective positions relative to the vertical direction pl) of said parameters making it possible to minimize a difference between the deformations of at least a part of the soft tissue observed from the images and the corresponding deformations determined by a model (U_( , p)) of the soft tissue which depends on said parameters. al and pl are thus values ​​taken by the fields a and p. The parameters al and pl can be determined for the whole of the soft tissue or for a part of the soft tissue.

[0023] Thus, in the invention it is possible to use a plurality of images, preferably biomedical, of a soft tissue placed in at least two different orientations relative to the vertical direction so as to use gravity, which is a perfectly known force, to identify several parameters of behavior, including at least the rigidity, and of loading, in particular the pressure, of a model of soft tissue subjected to loading.

[0024] By implementing the method according to the invention, the differences observed between the images obtained in different positions are mainly induced by gravity and can be used, within the framework of an inverse problem, to estimate the behavior of the tissues and the imposed loading.

[0025] By "soft tissue" is meant organic tissue on which gravity will have a significant effect. In other words, gravity causes a significant deformation of a soft tissue when its orientation is changed, for example a deformation of amplitude greater than or equal to 1%, 5% or 10% of at least one dimension of the soft tissue between two different orientations. A soft tissue can notably be a muscle, an organ or a fibrous tissue.

[0026] In an in vivo situation, pressure is difficult to measure non-invasively. The invention advantageously makes it possible to estimate not only the unloaded configuration of the organ and the stiffness of the tissue, but also the loading to which the organ is subjected. This makes it possible, in particular, to build higher-quality digital twins.

[0027] The invention also makes it possible to obtain more reliable values ​​of the parameters that can be estimated by existing methods.

[0028] Depending on the numerical models U( ,p) implemented, the parameterization of the stiffness field a can be a scalar parameter or several parameters, possibly spatialized, which can constitute a field of values. Similarly, the parameterization of the applied load p can be a scalar parameter or several parameters, possibly spatialized, which can constitute a field of values. According to an advantageous characteristic, at least one displacement fieldjmeas est determined from soft tissue images. The displacement field U_ meas characterizes the deformation of soft tissue between two positions by characterizing the changes in position of each material point between two images.

[0029] Preferably, the determination of the values ​​ci, pl of parameters minimizing said deviation is carried out by minimizing a function J ||, which corresponds to the displacement method. Other methods (deviation from equilibrium, error in behavioral relationship, virtual field method, etc.) can also be used.

[0030] The displacement field U_ meas can characterize the deformation of the entire soft tissue and can be fully determined, e.g. by image correlation method, before the determination of cri and pl; alternatively, t / meas , al and pl can be determined in a single integrated correlation or data assimilation step. The displacement field U meas can also be determined locally, i.e. on only one or more parts of the soft tissue, and the values ​​of cri and pl can be obtained for only these parts of the soft tissue.

[0031] Advantageously, the determination of the values ​​cri, pl of parameters minimizing said difference is carried out by the application of a statistical model, such as a neural network type model, to the images of the soft tissue or to a displacement field ( / mefïS ,jmeas £ tant determined from soft tissue images.

[0032] The statistical model used is configured, in particular trained, to determine the cri and pl values ​​either from the soft tissue images or from the displacement fields extracted from the images.

[0033] The statistical model can be a physics-informed neural network (PINN), which is particularly suitable for solving inverse problems involving physical data. The neural network can be trained by adapting the internal weights of the network so that it produces a good input-output relationship between the input data (which can be soft tissue images or the displacement fields obtained from soft tissue images) and the outputs, i.e., the ci and pl values. To this end, the neural network is evaluated for a large number of input data. The physical model of the soft tissue as well as the cost function characterizing the deviation between the model and the data are evaluated. The cost function is minimized by adapting the weights of the neural network.Once trained, the neural network is able to very quickly estimate the al and pl values ​​associated with a displacement field or images.

[0034] According to an advantageous characteristic, the method comprises, before determining the values ​​cri, pl of parameters minimizing said difference, a step of acquiring images of the soft tissue, in which the soft tissue is placed in a first position to acquire a first image then in a second position oriented differently with respect to the vertical direction to acquire a second image.

[0035] Preferably, the images are obtained by computed tomography, ultrasound and / or magnetic resonance imaging (MRI). More preferably, the soft tissue is an organ of a patient. The images of the soft tissue may in particular be acquired in vivo on the patient positioned at least in supination and pronation. The method may comprise the acquisition of the images.

[0036] The two images acquired with the soft tissue in different orientations correspond, for example, to images where the soft tissue has undergone a significant rotation between the two images, for example greater than 30°, in particular 90° or 180°. The method may comprise the step of modifying the orientation of a support on which the soft tissue rests, in a controlled manner, the acquisition of the images being carried out in connection with the control of the orientation of the support; the latter is, for example, a table on which a patient may rest.

[0037] The orientation change can be made around one or two horizontal geometric axes of rotation.

[0038] According to one embodiment of the invention, the soft tissue is a lung, a brain or a breast. The loading parameter may in particular be pleural pressure in the case of the lung and cerebral pressure in the case of the brain.

[0039] The invention also relates to a system for imaging the human or animal body configured to enable the acquisition of images of soft tissue of said body positioned in at least two different positions relative to the vertical, and comprising a processor executing a program making it possible to determine at least from these images said values ​​ci and pl by implementing the method according to the invention, as defined above.

[0040] The imaging system may be a tomographic, ultrasound, or MRI imaging system.

[0041] It may include a body reception surface whose orientation relative to the vertical can be modified, in particular automatically by the system, so as to change the orientation of the body between the acquisitions of the different images. This surface is, for example, a table rotating around one or two horizontal axes and capable of taking two differently oriented positions, for example at 90° to each other, for example each at 45° to the vertical.

[0042] The invention also relates to a computer program product comprising a code which, when executed on a processor, makes it possible to implement the different steps of the method according to the invention, as defined above.

[0043] The invention also relates to a simulator of the mechanical behavior of a soft tissue, comprising a digital twin of a soft tissue obtained by implementing the method according to the invention as defined above, this soft tissue being in particular a lung or the brain, and this digital twin being recorded in a computer memory. Such a simulator may comprise any computer system making it possible to exploit all of the data constituting the digital twin, in particular a microcomputer and / or a server, as well as an interface making it possible to interface this twin with a CAD tool for example.

[0044] The invention also relates to a method for manufacturing soft tissue protection equipment, in which a simulator as defined above is used in a phase of modeling the equipment to determine the mechanical stresses of the tissue in the event of mechanical stress through the equipment, and the equipment is manufactured after such a modeling phase. The modeling phase makes it possible, for example, to determine the shape and the material(s) of the equipment leading to optimization of the protection of the soft tissue, depending on manufacturing constraints for example.

[0045] Brief description of the drawings [Fig 1] Figure 1 shows different image acquisition schemes of a lung.

[0046] [Fig 2] Figure 2 is a graph representing the distribution of the error in identifying the stiffness of a structure as a function of the measurement noise, the identification being obtained by a known method using two supine images, where the stiffness and the loading are identified together.

[0047] [Fig 3] Figure 3 is a graph representing the distribution of the identification error of the pressure applied to a structure as a function of the measurement noise, the identification being obtained by a known method using two supine images, where the stiffness and the loading are identified together.

[0048] [Fig 4] Figure 4 is a graph representing the distribution of the error in identifying the stiffness of a structure as a function of the measurement noise, the identification being obtained by a known method using two prone images, where the stiffness and the loading are identified together.

[0049] [Fig 5] Figure 5 is a graph representing the distribution of the identification error of the pressure applied to a structure as a function of the measurement noise, the identification being obtained by a known method using two prone images, where the stiffness and the loading are identified together.

[0050] [Fig 6] Figure 6 is a graph representing the distribution of the error in identifying the stiffness of a structure as a function of the measurement noise, the identification being obtained by a method according to the invention using two prone images and two supine images, where the stiffness and the loading are identified together.

[0051] [Fig 7] Figure 7 is a graph representing the distribution of the identification error of the pressure applied to a structure as a function of the measurement noise, the identification being obtained by a method according to the invention using two prone images and two supine images, where the stiffness and the loading are identified together.

[0052] [Fig 8] Figure 8 is a graph showing the distribution of error in the identified stiffness of a lung as a function of noise as obtained by a known determination method using a supine image, the loading being known. [Fig 9] Figure 9 is a graph showing the distribution of error in the identified stiffness of the lung as a function of noise as obtained by a known determination method using a supine image, the loading being known.

[0053] [Fig 10] Figure 10 is a graph showing the distribution of error in identified lung stiffness versus noise as obtained by a determination method using a prone image and a supine image with known loading.

[0054] [Fig 11] Figure 11 represents an imaging system according to the invention.

[0055] Detailed description

[0056] In the context of the invention, the vertical direction is a direction parallel to the gravitational field.

[0057] In an advantageous embodiment, the invention is implemented in the context of the construction of a digital twin of a lung.

[0058] Figure 1 shows different image acquisition diagrams of a lung for implementing the method according to the invention. The orientation of the patient is defined by the arrow marked g indicating the direction of the gravitational field. An arrow pointing downwards in the figure corresponds, for example, to a pronation (or procubitus) position of the patient, while an arrow pointing upwards in the figure corresponds to a supination (or decubitus) position. The configurations of the lung at different times between the states of maximum expiration and maximum inspiration are marked pi to p n . The states p e and pi correspond respectively to the configuration of the lung in maximum expiration and in maximum inspiration. The displacement field between two states p a and pb is noted uy^bd ans the case of two pronation states, U a^bd ans i e cas I have two states in supination and U_ L P^ Sin the case of two pi states, the starting state being in the pronation position and the arrival state being in the supination position.

[0059] In the case of the lung, the deformation of the organ can be considered to be exclusively due on the one hand to pleural pressure, negative pressure ensuring that the lung remains inflated, and on the other hand to gravity, whose influence on the deformation is less compared to pleural pressure but nevertheless notable. Since the deformation of the lung is particularly sensitive to pleural pressure, it is important to have access to its precise value. Tissue stiffness is also a parameter that is important to identify in the context of this example. Indeed, stiffness could constitute an important biomarker allowing the diagnosis and prognosis of pulmonary diseases such as fibrosis. Two stiffnesses are then particularly interesting: healthy stiffness and fibrotic stiffness, higher due to the stiffening of the tissues induced by fibrosis.

[0060] In cases of lung disease, healthcare workers usually routinely acquire two images of the patient's lungs, both taken with the patient in the same position: one image at the end of expiration, and one image at the end of inspiration. This corresponds to case A shown in Figure 1.

[0061] Case A does not allow the estimation of pleural pressure, healthy stiffness and fibrotic stiffness at the same time, but only two of these quantities, for example healthy stiffness and fibrotic stiffness.

[0062] The method according to the invention uses images acquired in different positions of the patient, which in particular also makes it possible to estimate pleural pressure.

[0063] Case B presented in Figure 1 corresponds to the acquisition of three images: one image in the state of maximum inspiration in the pronation position and two images in the state of maximum expiration, one in the pronation position and the other in the supination position.

[0064] Case C presented in Figure 1 corresponds to the acquisition of four images: two images in the state of maximum inspiration and two images in the state of maximum expiration, one in the pronation position and the other in the supination position.

[0065] The use of a plurality of images, taken on a patient placed in at least two different vertical orientations, for example prone and decubitus, makes it possible to obtain more information on the behavior of the tissues and therefore to increase the number of identifiable parameters, or the precision of the estimation.

[0066] Thus, the images obtained in case B make it possible to obtain the field of displacements between the configuration at the end of expiration and at the end of inspiration in pronation, as well as the field of displacements between the configuration at the end of expiration in pronation and the configuration at the end of expiration in supination, due solely to gravity. Similarly, case C makes it possible to obtain the field of displacements between the configuration at the end of expiration and at the end of inspiration in pronation, as well as the field of displacements between the configuration at the end of expiration and at the end of inspiration in supination. The difference between these two fields is solely due to gravity. The data are then assimilated into an adapted model, thus resulting in a personalized model, i.e. a digital twin.

[0067] A numerical model, for example a finite element model, of the lung is then constructed from the information obtained from the images, in particular the geometry of the organ and the porosity field in this example. The images obtained provide access to the porosity field of the lungs. Considering that the latter are porous and that a solid phase comprising the tissues and the blood coexists with a fluid phase comprising the air circulating in the lungs, a so-called poromechanical law is advantageously formulated in this embodiment to model the lung.

[0068] La loi poromécanique utilisée peut être celle décrite dans les publications Patte, C., Genet, M., & Chapelle, D. (2022). A quasi-static poromechanical model of the lungs. Biomechanics and Modeling in Mechanobiology, 21(2), 527-551, Patte, C., Brillet, P. Y., Fetita, C., Bernaudin, J. F., Gille, T., Nunes, H., ... & Genet, M. (2022). Estimation of regional pulmonary compliance in idiopathic pulmonary fibrosis based on personalized lung poromechanical modeling. Journal of Biomechanical Engineering, 144(9), 091008, et Laville, C., Fetita, C., Gille, T., Brillet, P. Y., Nunes, H., Bernaudin, J. F., & Genet, M. (2023). Comparison of optimization parametrizations for regional lung compliance estimation using personalized pulmonary poromechanical modeling. Biomechanics and Modeling in Mechanobiology, 1-13.

[0069] Other laws can also be chosen depending on the compromise between accuracy and complexity of the desired model. For example, a hyperelastic law such as an Ogden-Ciarlet-Geymonat law or a Mooney-Rivlin law can be used. These laws are described in the publications Ogden, R.W. (1972). Large deformation isotropy elasticity: On the correlation of theory and experiment for compressible rubberlike solids. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 328(1575), 567-583, Ciarlet, P.G., & Geymonat, G. (1982). On the behavior laws of compressible nonlinear elasticity. Comptes Rendus de l'Académie Des Sciences Série II, 295, 423 — 426, and Weiss, J.A., Maker, B.N., & Govindjee, S. (1996). Finite element implementation of incompressible, transversely isotropic hyperelasticity. Computer Methods in Applied Mechanics and Engineering, 135(1-2), 107-128.The various parameters and pleural pressure are then estimated via an estimation step. This step is based in this embodiment on the FEMU method, also known as the displacement method. However, other estimation methods can be used such as the equilibrium deviation method or the virtual field method. These methods are described in Avril, S., Bonnet, M., Bretelle, A.S., Grédiac, M., Hild, F., lenny, P., ... & Pierron, F. (2008). Overview of identification methods of mechanical parameters based on full-field measurements. Experimental Mechanics, 48, 381-402.

[0070] Here we note 0 the behavior and loading parameters (including the applied pressure) to be identified.

[0071] The field of displacements between the configuration at the end of expiration and the configuration at the end of inspiration constitutes the measurement U_ measThe objective of the estimation step with the FEMU method is to find the parameters 0 which minimize the gap between P 7160 - 5 and the field of displacements calculated with the numerical model of the lung which depends on the parameters 0, which we note 1 / (0).

[0072] This is advantageously done by minimizing a function called the cost function In this embodiment, J is a discrete function. This function can be minimized with a classical derivative-free optimization algorithm, but any known optimization method could also be used.

[0073] Other cost functions can be used to determine the optimal 0 parameters. They can be based on the principle of deviation from equilibrium or directly on the intensity of the images.

[0074] The articles Allaire, G. (2007). Numerical analysis and optimization: An introduction to mathematical modeling and numerical simulation. Oxford University Press and Bard, Y. (1974). Nonlinear parameter estimation (No. 04; QA276. 8, B3.) describe different methods for minimizing a cost function.

[0075] Alternatively, the parameters are estimated by implementing a statistical model, such as a neural network type model, to obtain the parameters directly from the soft tissue images or from the displacement field determined from the soft tissue images. The method according to the invention is generalized to the case where there are more than two images and / or more than two orientations of the soft tissue relative to the vertical direction. The use of more than two images makes it possible to obtain a plurality of displacement fields U_ measby comparing the images two by two and thus improving the precision of the estimation of the optimal 0 parameters, or even allowing the identification of additional parameters.

[0076] Examples

[0077] In one example, synthetic data from a lung are used to validate the invention. While the invention makes it possible to identify parameters from real data measured on an individual, it is difficult to quantify the error made on the identified parameters because the exact values ​​corresponding to the real situation are not known. Thus, in this example, the inventors carried out the validation of the method according to the invention using synthetically generated data.

[0078] For this purpose, two synthetic measurements are created, one corresponding to a measurement of the displacement field between the end-of-expiration state and the end-of-inspiration state in the supine position and the other corresponding to a measurement of the displacement field between the end-of-expiration state and the end-of-inspiration state in the supine position. For this, the parameters 0 are set to physiological values ​​0 O and the associated displacement field is calculated via the numerical model of the lung used.

[0079] The resulting displacement field is perturbed by random Gaussian noise to account for the characteristic noise of real measurements, which may have various origins, for example, from the imaging equipment used. The intensity of the perturbation is characterized by the signal-to-noise ratio, denoted SNR. The smaller the SNR, the greater the impact of the noise on the images.

[0080] For a given SNR, several parameter estimations are carried out until the distribution of the identified parameter converges. The previously described optimization process is then applied.

[0081] In another example, a simplified linear spring model is used. This example corresponds to a highly identifiable case, for which the expected results are known. In this model, the displacement of the spring relative to an unloaded configuration depends on the ratio between the loading and the stiffness. The displacement between two positions of different vertical orientation depends on the orientation of the spring relative to gravity. Thus, the stiffness and the loading can take any value.

[0082] 1p— ma ii ' i respecting the ratio u = — - — where u corresponds to the displacement, p to the loading, ma to the mass, g to the acceleration of gravity and a to the stiffness, in the case of the prone position. In the In the case of the supine position, we obtain u = — - — . The optimization process here amounts to finding parameters (a, p) which allow us to approach u(a, p) as closely as possible to a given displacement u0. Thus, any loading p respecting the condition p = au0+ mg, for any stiffness value a, allows us to obtain the measurement u0. There are therefore an infinite number of pairs (c , p) = (a, au0+ mg) satisfying u = u0. It is therefore impossible to identify both the stiffness and the loading in the case of images obtained only on the back or only on the stomach.

[0083] The invention makes it possible to make these two parameters identifiable. Indeed, the difference between the displacement obtained in the case of the supine position and the displacement obtained in the case of the prone position is due to gravity. Using the images in both positions therefore allows access to additional information, thus allowing the identification of stiffness and loading.

[0084] Figures 2 to 7 illustrate these results.

[0085] Figures 2 and 4 represent the distribution of the error, denoted e, on the identified stiffness as a function of the measurement noise, denoted SNR, by applying a determination method on supine images (curve fl, figure 2) and on prone images (curve f3, figure 4). Figure 6 represents the distribution of the error e on the identified stiffness as a function of the SNR noise by applying the method according to the invention on prone and supine images (curve f5, figure 6).

[0086] Figures 3, 5, 7 represent the distribution of the error, noted e, on the identified loading as a function of the measurement noise, noted SNR, by applying a determination method on images in the supine position (curve f2, figure 3), on images in the prone position (curve f4, figure 5), and by applying the method according to the invention on images in the supine position and prone position (curve f6, figure 7).

[0087] The standard deviation G of the error distribution around the mean values ​​represented by curves fl to f6 is also shown in each of Figures 2 to 7.

[0088] For each of Figures 2 to 7, the curve d corresponds to the initial distribution, i.e. the values ​​at which the parameters are initialized before optimization. It is preferable to initialize the parameter values ​​in an interval close to the average values ​​of the parameters, for example plus or minus 30% around a known average value of the parameters. This makes it possible, in the case of in silico illustrations, to avoid an initialization systematically close to the exact solution and therefore to avoid distorted results; ultimately this corresponds to realistic cases of estimation where the real value is not known and cannot be used as an initialization.

[0089] It can be seen that for low noise levels typical of real measurements (SNR varying from plus infinity to 10), it is possible to identify both stiffness and loading with the method according to the invention (curves f5, f6). However, identification becomes impossible for small SNRs, because in such cases, the measurement is completely disrupted by noise.

[0090] On the other hand, whatever the noise level, we note that it is impossible to correctly identify both the stiffness and the loading in the case of a single measurement in the supine position and in the case of a single measurement in the prone position: the curves fl to f4 do not converge towards the correct value of the stiffness and the loading.

[0091] Adding images in an additional position therefore makes it possible to identify an additional parameter and thus improve the models developed by making them more personalized to each patient.

[0092] For comparison, Figures 8 to 10 represent the distribution of the error, noted e, on the identified stiffness as a function of the measurement noise, noted SNR, for a loading assumed to be known, by applying a determination method on supine images (curve f7, Figure 8) and on prone images (curve f8, Figure 9), as well as by applying the method according to the invention on prone and supine images (curve f9, Figure 10). It is clear from these graphs that a satisfactory identification of the stiffness is possible on the basis of a single image when the loading is known, the determination of the stiffness being improved by using both images. But, as illustrated in Figures 2 to 7, the identification of both the stiffness and the loading is not possible on the basis of a single image. The method according to the invention makes it possible to determine the stiffness and the loading in this case.Other variations and improvements may be provided without departing from the scope of the invention.

[0093] In particular, the method according to the invention can be applied to a number of images of the soft tissue greater than two. The images can also be taken when the soft tissue is in different configurations. For example, a lung in vivo has a different configuration at the end of inspiration and at the end of expiration. As described with reference to Figure 1, it is possible to compare two images of the lung at the end of inspiration and two images of the lung at the end of expiration, the images being taken in the prone and decubitus positions. It is also possible to use three images, as illustrated in case B of Figure 1, for example one image at the end of expiration and one image at the end of inspiration in the prone position and one image at the end of expiration in the decubitus position.

[0094] It is possible to use a larger number of images to provide a more detailed modeling of the soft tissue. This is particularly advantageous in the context of pulmonary fibrosis. Pulmonary fibrosis is characterized by non-homogeneous stiffening of lung tissue. Thus, in fibrosed lungs, there are several sections with different stiffnesses. By increasing the number of images used, the different stiffnesses can be better identified by allowing the measurement of more displacement fields between two images among the images used.

[0095] The invention requires images of the soft tissue to be taken in at least two different orientations relative to the vertical direction. These orientations are not limited to pronation and supination positions. A soft tissue, or a patient for in vivo measurements, may be oriented at different angles relative to the vertical when taking images. For example, a patient may be lying on a table when taking images in pronation and / or supination, and the table may be held horizontally and / or tilted by rotation about one or two horizontal axes perpendicular to each other. The rotation of the table about a horizontal axis may in particular be between 0° and 45°. Advantageously, the movement of the table facilitates the acquisition of the different images and the positioning of the patient, in particular when the patient is with reduced mobility or unconscious.

[0096] Figure 11 represents an imaging system 10 according to the invention. The imaging system 10 can in particular be used to acquire images of soft tissue of an animal or a human and can be a tomographic, ultrasound or MRI imaging system. It comprises an imaging device 11 and a receiving surface 12, for example a table, intended to receive the patient 13.

[0097] The receiving surface is, in the illustrated example, rotatable about a horizontal axis so as to be able to take different positions in which the orientation of the patient 13 relative to the vertical direction is different.

[0098] The invention is not limited to the lung. In particular, it is also applicable to the brain and facilitates the classification, diagnosis, prognosis, and treatment of brain diseases. It can also facilitate the detection of head trauma through rapid estimation of cranial pressure.

[0099] The brain is composed of soft tissues, on which gravity has a significant influence. It is subject to cranial pressure, the estimation of which in vivo, carried out via a lumbar puncture, is highly invasive. Unlike the lung, for which a displacement field is accessible in a single position (by comparing images at the end of expiration and at the end of inspiration, for example) thanks to the pleural pressure differential, the cranial pressure remains constant. The use of gravity therefore makes it possible to access a displacement field which, thanks to the method according to the invention, makes it possible to identify both parameters such as tissue rigidity and cranial pressure.

[0100] The invention makes it possible to obtain a more reliable model of the brain through better identification of the model's parameters. This can, for example, help with the sizing of sports equipment, in particular protective helmets for sports involving risks of head trauma such as rugby or American football. Indeed, the invention can help estimate the increase in cranial pressure following an impact depending on the configuration (material, dimensions, etc.) of the helmet.

[0101] More generally, the increase in pressure in the skull following an impact is a significant issue and is the subject of particular attention in the development of safety devices. For example, many safety devices in the automotive industry are developed using biomechanical models of the body, particularly the human head. A better estimation of cranial pressure values ​​following an impact allows for the design of more efficient safety equipment. Biomechanical modeling is an important step in the manufacturing of protective equipment. Indeed, it allows for in silico testing and optimization of the topology and geometry of this equipment, which reduces the costs associated with physical models.Furthermore, physical tests are performed on dummies whose physical properties may differ from those of humans, and they do not provide access to quantities of interest such as the increase in cranial pressure following an impact. Coupling a model of equipment, for example a helmet, with a model of the brain would improve access to this information. Indeed, modeling an impact on a helmet provides access to stresses transmitted to the brain, which then makes it possible to determine potential damage. Identifying stiffness and pressure parameters in the brain could therefore help optimize the manufacture of a personalized helmet that best protects people such as professional athletes.

[0102] More broadly, the method according to the invention can be applied to all objects or soft tissues, whether human, animal or plant, to non-invasively estimate internal rigidities and pressures from volumetric images without requiring force measurement. This has numerous applications such as the classification of diseases from identified pressure values, diagnostic assistance or the sizing of protective or safety equipment.

Claims

Claims 1. Computer-implemented method for determining parameters comprising a stiffness field of a soft tissue (a) and a loading parameter (p) applied to the soft tissue, in particular a pressure field, in which the values ​​pl) of said parameters are determined from at least two images of this soft tissue oriented in at least two different respective positions relative to the vertical direction making it possible to minimize a difference between the deformations of at least part of the soft tissue observed from the images and the corresponding deformations determined by a model (U_ a, p~)) of the soft tissue which depends on said parameters.

2. Method according to claim 1, in which a displacement field jmeas est determined from the soft tissue images and the determination of the values ​​(cri, pl) of parameters minimizing said deviation is carried out by minimizing a function 3. Method according to claim 1, in which the determination of the values ​​(cri, pl) of parameters minimizing said deviation is carried out by the application of a statistical model, such as a neural network type model, to the images of the soft tissue or to a displacement field t / meas , jjmeas ^ tant determined from soft tissue images.

4. Method according to one of the preceding claims, comprising before determining the values ​​(cri, pl) of parameters minimizing said difference a step of acquiring images of the soft tissue, in which the soft tissue is placed in a first position to acquire a first image then in a second position oriented differently with respect to the vertical direction to acquire a second image.

5. Method according to the preceding claim, the images being obtained by computed tomography, by ultrasound echography and / or by magnetic resonance imaging.

6. Method according to the preceding claim, the soft tissue being an organ of a patient.

7. Method according to the preceding claim, the images of the soft tissue being acquired in vivo on the patient positioned at least in supination and in pronation.

8. Method according to one of the preceding claims, the soft tissue being a lung, a brain or a breast.

9. Imaging system (10) of the human or animal body configured to allow the acquisition of images of a soft tissue of said body (13) positioned in at least two different positions relative to the vertical, and comprising a processor executing a program making it possible to determine at least from these images said values ​​(al, pl) of parameters by implementing the method according to any one of the preceding claims.

10. Imaging system according to claim 9, being a tomographic, ultrasound or MRI imaging system.

11. System according to claim 9 or 10, comprising a receiving surface (12) for the body whose orientation relative to the vertical can be modified, in particular automatically by the system, so as to change the orientation of the body between the acquisitions of the different images, this surface being in particular a table rotating around one or two horizontal axes and capable of taking two differently oriented positions, for example at 90° to each other, for example each at 45° to the vertical.

12. Computer program product comprising code which, when executed on a processor, implements the different steps of the method as defined in any one of claims 1 to 8.

13. Simulator of the mechanical behavior of a soft tissue, comprising a digital twin of a soft tissue obtained by implementing the method according to any one of claims 1 to 8, this soft tissue being in particular a lung or the brain, and this digital twin being recorded in a computer memory.

14. Method for manufacturing soft tissue protection equipment, in which a simulator as defined in claim 13 is used in a modeling phase of the equipment to determine the mechanical stresses of the tissue in the event of mechanical stress through the equipment, and the equipment is manufactured after such a modeling phase.

Images